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On the Cadlaguity of Random Measures
Robert J. Adler and Paul D. Feigin
The Annals of Probability
Vol. 12, No. 2 (May, 1984), pp. 615-630
Published by: Institute of Mathematical Statistics
Stable URL: http://www.jstor.org/stable/2243491
Page Count: 16
You can always find the topics here!Topics: Entropy, Borel sets, Stochastic processes, Mathematical inequalities, Rectangles, Random variables, Eigenfunctions, Additivity, Indicator functions, Real lines
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We consider finitely additive random measures taking independent values on disjoint Borel sets in Rk, and ask when such measures, restricted to some subclass A of closed Borel sets, possess versions which are "right continuous with left limits", in an appropriate sense. The answer involves a delicate relationship between the "Levy measure" of the random measure and the size of A, as measured via an entropy condition. Examples involving stable measures, Dudley's class I(k, α, M) of sets in Rk with α-times differentiable boundaries, and convex sets are considered as special cases, and an example given to show what can go wrong when the entropy of A is too large.
The Annals of Probability © 1984 Institute of Mathematical Statistics